State Estimation in Hybrid Systems with a Bounded Number of Mode Transitions in the Presence of Spurious Measurements

摘要

We consider the problem of tracking the state of a hybrid system ca-pable of performing a bounded number of mode transitions in the pres-ence of spurious, or cluttered measurements. The system is assumed tofollow, at each time, one of a predefined dynamical models. Two types ofuncertainties make the problem challenging. The first is the data uncer-tainty that follows from the fact that the true measurement of the stateis indistinguishable from the clutter measurements that do not carryuseful information. The second problem is the intrinsic model uncer-tainty. Both reasons prevent the computation of the optimal estimator.On the other hand, the mode transitions are not Markov thus rulingout the direct use of standard approaches for state estimation in clut-tered environment. We derive an efficient estimation scheme for systemsin cluttered environments capable of performing a bounded number ofmode transitions. At the heart of this scheme is a transformation of thenon-Markov model set to an equivalent Markovian one and a subsequentutilization of standard approaches matched to the new mode set. Thealgorithm’s performance is evaluated via a simulation study, and shownto outperform the standard popular approaches in a typical example.